Answer: ∠AOB=112°
Step-by-step explanation:
- Central Angle Property. An inscribed angle is half the measure of a central angle subtended by the same arc. A central angle is twice the measure of an inscribed angle subtended by the same arc. COB since both are subtended by arc(CB)
Then in our case ∠AOB -central ; ∠ACB= inscribed
Then :
let ∠AOB=2∠ACB=2α ; ∠ACB=α
Then :
∠COA+∠COB+2α=360 (because the full angle is O)
∠СOA+∠COB=360-2α
And we know :
∠СOA+∠COB+∠CAO+∠ACB+∠CBO=360
360-2α+α+∠CAO+∠CBO=360
360-a=360-∠CAO-∠CBO
[tex]\boxed{\angle ACB=\alpha =\angle CAO+\angle CBO} } \sf - \\\\This \ formula always \ works \ , \ the \ main \ thing \ is \ to \ remember \ it[/tex]
Then :
α=(32+24)=56° ; ∠AOB=2α=56*2=112°
